3.2 OLTC centralized control

of DGs changes the voltage profile significantly and complicates the voltage regulation. This is due to two reasons: (i) the voltage trend not descending from the substation to the feeder terminal, thereby invalidating the target point (reference) and (ii) the voltage estimation, based on local measurements, becoming inaccurate because of the stochastic power natures of RES and EVs [13]. Moreover, the stochastic power nature of EVs makes the voltage estimation inferior and aggravates the undervoltage problem. Therefore, OLTCs may suffer from wear and tear due to excessive operations. This problem worsens when feeders suffer from overvoltage due to high DG penetration, while others suffer from undervoltage during high demand, such as PEV charging. In this instance, the OLTC will have two

Figure 5.

Figure 6.

60

DG and PEV power profiles.

Simplified distribution network with DG and PEVs.

Research Trends and Challenges in Smart Grids

contradicting solutions. Increasing the transformer's secondary voltage mitigates the undervoltage problem at the expense of the system's overvoltage and vice versa. Figure 6 shows two daily power profiles for uncontrolled<sup>1</sup> PEV charging demand and a PV-based DG. The PEV demand is generated based on practical arrival/ departure times from the Toronto Parking Authority (TPA), Toronto, Canada. Since the power profiles of commercial parking lots and PV-based DGs naturally coincide, there is a high chance that the system simultaneously suffers from overvoltage and undervoltage. A partial solution for this problem can be realized if a centralized-based controller for the OLTC exploits the system's maximum and minimum voltages. However, this controller may not prevent the OLTC hunting

<sup>1</sup> In uncontrolled charging schemes, PEVs start charging as soon as they are plugged in.

As shown in Figure 7, the OLTC is represented by a π-circuit model [14]. The taps are assumed to be at the primary side (high voltage). Subsequently, the OLTC secondary voltage and current can be calculated by

$$
\begin{bmatrix} V\_{(1,t)} \\ I\_{(1,t)} \end{bmatrix} = \begin{bmatrix} \mathbf{1} & -\frac{a}{\mathbf{Y}\_T} \\ a & -\mathbf{y}\_T \\ \mathbf{0} & -a \end{bmatrix} \begin{bmatrix} V\_{(0,t)} \\ I'\_{(0,t)} \end{bmatrix} \tag{27}
$$

where Y<sup>T</sup> is the transformer series admittance, a is the turns ratio given in (2), and t denotes the time instant. To take the physical busses into account, (27) can be rewritten as

$$
\begin{bmatrix} I\_{(0,t)} \\ I\_{(1,t)} \end{bmatrix} = \underbrace{\begin{bmatrix} g\_F + jb\_\mu + \frac{Y\_T}{a^2} & -\frac{Y\_T}{a} \\ -\frac{Y\_T}{a} & Y\_T \end{bmatrix}}\_{\text{Yourc}} \begin{bmatrix} V\_{(0,t)} \\ V\_{(1,t)} \end{bmatrix} \tag{28}
$$

where YOLTC is the OLTC Y-bus admittance matrix, which represents the OLTC admittance in the power flow equations.

The conventional OLTC controller, shown in Figure 8(a), is modified to emulate an adaptive reference by considering the system's minimum and maximum voltages, that is, Vsys minand Vsys max, respectively. This modification forms the centralized OLTC controllers (COC) proposed in [13] and shown in Figure 8(b), which

Figure 7. Equivalent π-circuit model of OLTC.

Figure 8. The OLTC control: (a) conventional local controller and (b) centralized OLTC controller (COC).

allows the OLTC to deal with multiple feeders with voltage problems resulted from DGs and PEVs. The COC emulates an adaptive reference because the error ΔVchanges such that Vsys minand Vsys max are within the standard limitsVUpper and VLower (i.e., 1.05 and 0.95 p.u.), respectively. Vsys min and Vsys max can be estimated using the state estimation algorithm in [15] or attained through the central voltage control unit explained in the next subsection.

In the case of an overvoltage, ΔV is negative, and the primary controller decreases the transformer secondary voltage (by increasing the tap position) and vice versa. During normal conditions, ΔV is zero because both Vsys min and Vsys max are within the standard limits; thus, the tap position remains unchanged. When both overvoltage and undervoltage occur simultaneously, the COC should be disabled to avoid hunting [16]. In the next subsection, the roles of DGs and PEVs in voltage regulation are explained to mitigate the shortcoming of the COC.

3.3.1 Problem formulation of stage (I)

PEV/DG voltage support scheme.

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DOI: http://dx.doi.org/10.5772/intechopen.85108

owners, that is,

Figure 9.

63

take the following form:

where <sup>X</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> and <sup>Q</sup>PEV

The main objective of Stage (I) is maximizing the energy delivered to PEV

∑ chð Þ<sup>i</sup> ∈CHð Þ<sup>i</sup>

where EDð Þ ch ið Þ;<sup>t</sup> is the energy delivered to the PEV connected to charger chð Þ<sup>i</sup> ∈CHð Þ<sup>i</sup> at PEV bus i ∈I PEV, I PEV is the set of busses with PEV charger connections, CHð Þ<sup>i</sup> is the set of chargers connected to bus i, and γ is the decision variable vector. The PEV and DG voltage support depends mainly on γ, which can generally

power at bus i∈ IPEV, respectively; Po ið Þ ;<sup>t</sup> and Qo ið Þ ;<sup>t</sup> are the DG active and reactive

o ið Þ ;<sup>t</sup> ; Po ið Þ ;<sup>t</sup> ; Qo ið Þ;<sup>t</sup>

h i (30)

o ið Þ ;<sup>t</sup> are the vector of the charger decisions and PEV reactive

<sup>γ</sup> <sup>¼</sup> <sup>X</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> ; <sup>Q</sup>PEV

powers at bus i ∈I DG, respectively; and I DG is the set of busses with DG

ED chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>∀</sup><sup>t</sup> (29)

max<sup>γ</sup> <sup>∑</sup> i∈IPEV

#### 3.3 Optimal coordinated voltage regulation

Both power electronic converters of PEVs and DGs can support the grid with reactive power to relax the OLTC. A vehicle-to-grid reactive power support (V2GQ) strategy is proposed in [13] to incorporate PEVs and DGs in voltage regulation, as shown in Figure 9. The main difference between vehicle-to-grid (V2G) strategies and the V2GQ is that the latter injects only reactive power to the grid. Thus, it preserves the battery life of PEV, that is, the highest priority of the vehicles' owners. Nevertheless, the V2GQ cannot be flexibly employed in power management because PEVs do not export active power to the grid. V2G strategies are avoided in voltage regulation to elongate the battery life, which is considered a priority in this study. The V2GQ comprises a three-stage nonlinear programming, in which Stage (I) aims at maximizing the energy delivered to PEVs, Stage (II) minimizes the DG active power curtailment, and Stage (III) minimizes the voltage deviations. The COC is coordinated such that it acts after Stage (III) to ensure that all bus voltages are within the standard limits.

Voltage Regulation in Smart Grids DOI: http://dx.doi.org/10.5772/intechopen.85108

Figure 9. PEV/DG voltage support scheme.

allows the OLTC to deal with multiple feeders with voltage problems resulted from

state estimation algorithm in [15] or attained through the central voltage control

In the case of an overvoltage, ΔV is negative, and the primary controller decreases the transformer secondary voltage (by increasing the tap position) and

within the standard limits; thus, the tap position remains unchanged. When both overvoltage and undervoltage occur simultaneously, the COC should be disabled to avoid hunting [16]. In the next subsection, the roles of DGs and PEVs in voltage

Both power electronic converters of PEVs and DGs can support the grid with

reactive power to relax the OLTC. A vehicle-to-grid reactive power support (V2GQ) strategy is proposed in [13] to incorporate PEVs and DGs in voltage regulation, as shown in Figure 9. The main difference between vehicle-to-grid (V2G) strategies and the V2GQ is that the latter injects only reactive power to the grid. Thus, it preserves the battery life of PEV, that is, the highest priority of the vehicles' owners. Nevertheless, the V2GQ cannot be flexibly employed in power management because PEVs do not export active power to the grid. V2G strategies are avoided in voltage regulation to elongate the battery life, which is considered a priority in this study. The V2GQ comprises a three-stage nonlinear programming, in which Stage (I) aims at maximizing the energy delivered to PEVs, Stage (II) minimizes the DG active power curtailment, and Stage (III) minimizes the voltage deviations. The COC is coordinated such that it acts after Stage (III) to ensure that

vice versa. During normal conditions, ΔV is zero because both Vsys

regulation are explained to mitigate the shortcoming of the COC.

min and Vsys

max are within the standard limitsVUpper and VLower

max can be estimated using the

min and Vsys

max are

DGs and PEVs. The COC emulates an adaptive reference because the error

The OLTC control: (a) conventional local controller and (b) centralized OLTC controller (COC).

minand Vsys

(i.e., 1.05 and 0.95 p.u.), respectively. Vsys

Research Trends and Challenges in Smart Grids

3.3 Optimal coordinated voltage regulation

all bus voltages are within the standard limits.

unit explained in the next subsection.

ΔVchanges such that Vsys

Figure 8.

62

#### 3.3.1 Problem formulation of stage (I)

The main objective of Stage (I) is maximizing the energy delivered to PEV owners, that is,

$$\max\_{\mathcal{T}} \sum\_{i \in \mathcal{T}\_{\text{PHV}}} \sum\_{ch\_{(i)} \in \mathcal{CH}\_{(i)}} E\_{D\left(ch\_{(i)}, t\right)} \qquad \forall t \tag{29}$$

where EDð Þ ch ið Þ;<sup>t</sup> is the energy delivered to the PEV connected to charger chð Þ<sup>i</sup> ∈CHð Þ<sup>i</sup> at PEV bus i ∈I PEV, IPEV is the set of busses with PEV charger connections, CHð Þ<sup>i</sup> is the set of chargers connected to bus i, and γ is the decision variable vector. The PEV and DG voltage support depends mainly on γ, which can generally take the following form:

$$\chi = \left[ \mathbb{X}\_{\left(ch\_{(i)}, t\right)}, \mathbb{Q}\_{o(i,t)}^{\text{PEV}}, P\_{o(i,t)}, Q\_{o(i,t)} \right] \tag{30}$$

where <sup>X</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> and <sup>Q</sup>PEV o ið Þ ;<sup>t</sup> are the vector of the charger decisions and PEV reactive power at bus i∈ IPEV, respectively; Po ið Þ ;<sup>t</sup> and Qo ið Þ ;<sup>t</sup> are the DG active and reactive powers at bus i ∈I DG, respectively; and I DG is the set of busses with DG

connections. The charging decisions are continuous, that is, X ∈ ½ � 0; 1 where "0" stands for no charging and "1" stands for full charging. According to the grid operator, γ can be partially constrained. For instance, the PEV reactive powers can be set to zero, that is, QPEV o ið Þ ;<sup>t</sup> <sup>¼</sup> <sup>0</sup>, <sup>∀</sup>i<sup>∈</sup> <sup>I</sup>PEV, t, when the PEV voltage support is disregarded. Stage (I) should satisfy the power flow constraints, as given by

$$P\_{G(i,t)} - P\_{L(i,t)} = \sum\_{j \in \mathcal{I}\_b} V\_{(i,t)} V\_{(j,t)} Y\_{(i,j)} \cos \left(\theta\_{(i,j)} + \delta\_{(j,t)} - \delta\_{(i,t)}\right) \qquad \forall i \in \mathcal{I}\_b, t \tag{31}$$

$$Q\_{G(i,t)} - Q\_{L(i,t)} = \sum\_{j \in \mathcal{I}\_b} V\_{(i,t)} V\_{(j,t)} Y\_{(ij)} \sin \left( \theta\_{(ij)} + \delta\_{(j,t)} - \delta\_{(i,t)} \right) \qquad \forall i \in \mathcal{I}\_b, t \tag{32}$$

where PG ið Þ ;<sup>t</sup> and QG ið Þ ;<sup>t</sup> denote the generated active and reactive powers, respectively; PL ið Þ ;<sup>t</sup> and QL ið Þ ;<sup>t</sup> are the active and reactive power demands, respectively; Vð Þ <sup>i</sup>;<sup>t</sup> and δð Þ <sup>i</sup>;<sup>t</sup> denote the magnitude and angle of the voltage, respectively; I<sup>b</sup> is the set of system busses; and Yð Þ <sup>i</sup>;<sup>j</sup> and θð Þ <sup>i</sup>;<sup>j</sup> are the magnitude and angle of the Y-bus admittance matrix, respectively.

The voltage and feeder thermal limits should also hold, and thus,

$$V\_{\min} \le V\_{(i,t)} \le V\_{\max} \quad \forall i \in \mathcal{I}\_b, t \tag{33}$$

$$I\_{(l,t)} \le I\_{(l)}^{CAP}, \quad \forall l \in \mathcal{QC}, t \tag{34}$$

where Vmax

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DOI: http://dx.doi.org/10.5772/intechopen.85108

by the DC link voltage.

loads and PEV:

where PPEV

battery and SOCF

SOCF

65

ED chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>¼</sup> EBAT ch ð Þ ð Þ<sup>i</sup> �

chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>¼</sup> SOC<sup>I</sup>

by.

on solar insolation, whereas PPEV

PPEV

capacity of the charger, that is, PCH ≤PCharger

o ið Þ;<sup>t</sup> ¼ ∑

chð Þ<sup>i</sup> ∈CHð Þ<sup>i</sup>

characteristics of the battery, which can be expressed as

PCH chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>¼</sup> <sup>f</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> SOC<sup>F</sup>

delivered to a PEV battery and its SOC can be given by

chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>þ</sup>

SOCF

where EBAT ch ð Þ ð Þ<sup>i</sup> is the battery capacity in kWh and SOCI

initial SOC. The SOC of different PEVs are updated according to

c ið Þ represents the maximum converter voltage which depends on the

converter DC link voltage [17, 18], So ið Þ;<sup>t</sup> denotes the DG rated power, and Xð Þ<sup>i</sup> is the total reactance of the DG filter and interfacing transformer at bus i . If the DC/AC converter increases the set point for the DC link voltage to relax Constraint (38), the DC/DC converter will operate at a high duty cycle, which decreases its efficiency [19]. Hence, the reactive power support from the DC/AC converter is limited

The load power at a bus should be equal to the total power consumed by regular

o ið Þ ;<sup>t</sup> is the PEV active power and PNL ið Þ ;<sup>t</sup> and QNL ið Þ ;<sup>t</sup> are the active and

o ið Þ ;<sup>t</sup> depends on charging decisions <sup>X</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> , the

reactive powers of normal loads, respectively. The PV power profile relies mainly

charging power limit in kW PCH chð Þ<sup>i</sup> ð Þ;<sup>t</sup> , and the charging efficiency <sup>η</sup>CH ch i ð Þ ð Þ , as given

<sup>X</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> PCH chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>η</sup>CH ch ð Þ ð Þ<sup>i</sup> Sbase

where Sbase is the base power for the per-unit system in kW. The charging power limit PCH is a function of the PEV battery state of charge (SOC) and is limited by the

chð Þ<sup>i</sup> ð Þ;<sup>t</sup>

chð Þ<sup>i</sup> ð Þ;<sup>t</sup> is the reached SOC. The relationship between the energy

chð Þ<sup>i</sup> ð Þ;<sup>t</sup>

<sup>60</sup>

where <sup>f</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> is the function that represents the characteristics of the PEV

chð Þ<sup>i</sup> ð Þ;<sup>t</sup> � SOC<sup>I</sup>

<sup>X</sup> chð Þ<sup>i</sup> ð Þ;<sup>t</sup> PCH chð Þ<sup>i</sup> ð Þ;<sup>t</sup> <sup>Δ</sup><sup>T</sup>

EBAT ch ð Þ ð Þ<sup>i</sup>

where ΔT is the time step to collect the system data, run the program, and implement the decisions. Similar to DGs, the injected reactive powers from the PEVs should be limited by their converter ratings and DC link voltages, as given by

o ið Þ ;<sup>t</sup> , <sup>∀</sup><sup>i</sup> <sup>∈</sup>Ib, t (39)

o ið Þ ;<sup>t</sup> , <sup>∀</sup><sup>i</sup> <sup>∈</sup>Ib, t (40)

, ∀i ∈I PEV, t (41)

rated . This function is dependent on the

, <sup>∀</sup><sup>i</sup> <sup>∈</sup><sup>I</sup> PEV, chð Þ<sup>i</sup> , t (42)

<sup>100</sup> , <sup>∀</sup><sup>i</sup> <sup>∈</sup><sup>I</sup> PEV, chð Þ<sup>i</sup> , t (43)

chð Þ<sup>i</sup> ð Þ;<sup>t</sup> denotes the PEV

, ∀i∈ I PEV, chð Þ<sup>i</sup> , t (44)

PL ið Þ ;<sup>t</sup> <sup>¼</sup> PNL ið Þ ;<sup>t</sup> <sup>þ</sup> <sup>P</sup>PEV

QL ið Þ ;<sup>t</sup> <sup>¼</sup> QNL ið Þ ;<sup>t</sup> <sup>þ</sup> <sup>Q</sup>PEV

where Vmin and Vmax are the maximum and minimum voltage limits, that is, 0.9 and 1.1 p.u., respectively; Ið Þ <sup>l</sup>;<sup>t</sup> denotes the per-unit current through line l ∈ ℒ; ℒ is the set of system lines; and I CAP ð Þ<sup>l</sup> is the current carrying capacity.

Typically, two back-to-back power electronic converters are used to interface PEVs and PVs, that is, DC/DC and DC/AC converters. The DC/DC converter performs MPPT with PV-based DGs or controls the PEV charging. The DC/AC converter regulates the DC link voltage and is responsible for the reactive power support [7]. The power injected to a bus should be equal to the output power of the DG installed at that bus:

$$\begin{cases} P\_{G(i,t)} = P\_{o(i,t)} \\ Q\_{G(i,t)} = Q\_{o(i,t)} \end{cases}, \qquad \forall i \in \mathcal{I}\_{DG}, t \tag{35}$$

$$P\_{o(i,t)} \le P\_{o(i,t)}^{\text{MPPT}}, \qquad \forall i \in \mathcal{T}\_{DG}, t \tag{36}$$

where PMPPT o ið Þ ;<sup>t</sup> denotes the DG maximum power available. In both PEVs and PVs, the DC/AC converter is similar to that used with Typ. 4 wind farms. Therefore, the reactive power capability limits, defined in [17], should be used as constraints. These limits depend on the converter's power rating and DC link voltage, as follows:

$$\mathcal{Q}^2\_{o(i,t)} \le \mathcal{S}^2\_{o(i,t)} - P^2\_{o(i,t)}, \qquad \forall i \in \mathcal{T}\_{DG}, t \tag{37}$$

$$\left(\mathbf{Q}\_{o(i\mid t)} + \frac{V\_{(i\mid t)}^2}{X\_{(i\)}}\right)^2 \le \left(\frac{V\_{c(i)}^{\max} V\_{(i\mid t)}}{X\_{(i)}}\right)^2 - P\_{o(i\mid t)}^2, \qquad \forall i \in \mathcal{T}\_{\text{DG}}, t \tag{38}$$
